Growth vs Decay Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

A population grows by

8\%

per year. Starting at

5000

, write the growth function and find the population after

10

years.

1
Growth rate $r=0.08$ , so base $b=1+0.08=1.08$ . Function: $P(t)=5000\cdot(1.08)^t$ .
2
$P(10)=5000\cdot(1.08)^{10}\approx5000\cdot2.1589\approx10{,}795$ .

Answer

P(t)=5000\cdot(1.08)^t

;

P(10)\approx10{,}795

An annual growth rate of

r\%

corresponds to multiplying by

1+r/100

each year. After

t

years, the factor

(1+r/100)^t

compounds the growth.

About Growth vs Decay

Exponential growth occurs when a quantity multiplies by a factor $> 1$ repeatedly; exponential decay when it multiplies by a factor between 0 and 1.

Classify each function as growth or decay, and find its value at [formula]: (a) [formula], (b) [form

A radioactive substance has a half-life of [formula] years. Starting with [formula] g, write the dec

Show algebraically that [formula] is an exponential decay function by rewriting it in the form [form